Question

Select all terms that are equivalent to 4^34^5


Show your work.

(2 points)
Responses

1/4^2

4^2

4^−2

1/16

−4^2

Answer 1

To determine the terms that are equivalent to \(4^{3} \times 4^{5}\), we first need to simplify the expression.

Using the property of exponents that states \(a^m \times a^n = a^{m+n}\), we can simplify:

\[
4^{3} \times 4^{5} = 4^{3+5} = 4^{8}
\]

Now we will evaluate each of the given responses to see if any of them equal \(4^{8}\).

1. **Response: \( \frac{1}{4^2} \)**
\(\frac{1}{4^2} = 4^{-2}\)

2. **Response: \( 4^2 \)**
This is equal to \(4^2\), which is not equal to \(4^{8}\).

3. **Response: \( 4^{-2} \)**
This is equal to \(4^{-2}\), which is not equal to \(4^{8}\).

4. **Response: \( \frac{1}{16} \)**
Since \(16 = 4^2\), \(\frac{1}{16} = 4^{-2}\), which is not equal to \(4^{8}\).

5. **Response: \( -4^2 \)**
This is equal to \(-16\), which is not related to \(4^{8}\) in its exponent form.

After evaluating:

- The only equivalent form we generally consider for exponentials involving \(4\) would be multiples of the same base in the relevant exponent.
- However, none of the responses provided correspond in value or equivalence to \(4^{8}\).

Thus, none of the listed terms are equivalent to \(4^{3} \times 4^{5} = 4^{8}\).